The Force of Gravity

While the theory of Newtonian potentials has various aspects, it is best introduced as a body of results on the properties of forces which are characterized by Newtons Law of Universal Gravitation1: Every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distance from each other. If, however, potential theory were restricted in its applications to problems in gravitation alone, it could not hold the important place which it does, not only in mathematical physics, but in pure mathematics as well. In the physical world, we meet with forces of the same character acting between electric charges, and between the poles of magnets. But as we proceed, it will become evident that potential theory may also be regarded as the theory of a certain differential equation, known as LAPLACE’S. This differential equation characterizes the steady flow of heat in homogeneous media, it characterizes the steady flow of ideal fluids, of steady electric currents, and it occurs fundamentally in the study of the equilibrium of elastic solids.